Elastodynamic Green's function for reinforced concrete beams

Abstract

A semi-analytical solution procedure for three dimensional wave propagation in reinforced concrete (RC) beams has been presented in this paper. Elastodynamic Green's function has been derived by employing the compatibility conditions and utilizing the symmetry conditions at the loaded cross section. Numerical procedure developed for the Green's function has been validated using results available in the literature for an infinite laminated composite plate. Three-dimensional wave propagation analysis has been performed for reinforced concrete beam sections of T and L shapes which are common forms of structural elements. Steel reinforcement has been modeled in the finite element mesh. Effect of corrosion has also been included in the finite element model. Green's function for reinforced concrete sections affected by corrosion of steel unit normalized frequency has been evaluated for illustration. Accuracy of the solution technique has been evaluated in terms of the percentage error in energy balance between the input energy of the applied unit load and the output energy carried by the propagating wave modes. The percentage error has been found to be negligible in all the cases considered here. A simple and accurate numerical method has been presented here as a tool to evaluate Green's function for RC beams and can be used to detect corrosion.